Related papers: Nonassociative geometry: Friedmann-Robertson-Walke…
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An…
I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant…
We study a non-relativistic realisation of two-dimensional de Sitter gravity both from its boundary and bulk description with the goal of learning about de Sitter space and paving the way for extending the holographic duality into a…
Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…
We study the dynamics of Friedmann-Lema\^itre-Robertson-Walker models where a dark energy component with a quadratic equation of state (EoS) nonlinearly interacts with cold dark matter. Thus, two energy scales naturally come into play:…
We introduce a class of brane-world models in which a single brane is embedded in an anti-de Sitter spacetime containing a rotating (Kerr) black hole. In this Letter we consider the case of slow rotation, calculating the metric and dynamics…
We provide a detailed analysis of Friedmann-Robertson-Walker universes in a wide range of scalar-tensor theories of gravity. We apply solution-generating methods to three parametrised classes of scalar-tensor theory which lead naturally to…
We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales. Two special cases, namely dicrete pseudospherical surfaces and smooth pseudosperical surfaces are consistent with this description. In…
The question of existence of general, asymptotically flat radiative spacetimes and examples of explicit classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. The examples are…
We investigate the cosmic dynamics of Rastall gravity in non-flat Friedmann-Robertson-Walker (FRW) space-time with barotropic fluid. In this context, we are concerned about the class of model satisfying the affine equation of state. We…
We investigate the cosmological dynamics in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry in scalar-tensor and scalar-torsion theories where the nonminimally coupled scalar field is a complex field. We derive the…
In this paper we define and analyze singularities of discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms. In particular, we discuss singularities of discrete…
The existence of self-similar solutions is discussed in symmetric teleparallel $f(Q)$-theory for a Friedmann-Lema\^itre-Robertson-Walker background geometry with zero and non-zero spatial curvature. For the four distinct families of…
The aim of the present paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson-Walker spacetime is a perfect fluid spacetime.…
We investigate measures of distance and redshift in cosmological space-times that admit a shear-free foliation, which we henceforth refer to as `quasi-Newtonian'. Space expands isotropically in this description, and small-scale…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
The objective of the present paper is to study 4-dimensional almost pseudo Ricci symmetric perfect fluid spacetimes $(APRS)_4$. We show that a Robertson-Walker spacetime is $(APRS)_4$ and vice versa under certain condition imposed on its…